Lets suppose x = senior citizens and y = adults. So we create a system of equations:
\(12x+14.5y = 3470\)
\(x+y=260\)
Then we solve the system of equations:
\(12x+14.5y = 3470\)
\(12x+12y=3120\)
Then we subtract:
\(2.5y=350\)
Divide:
\(y=140\)
And then we can solve for x:
\(x=120\)
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